منابع مشابه
A Note on Forbidding Clique Immersions
Robertson and Seymour proved that the relation of graph immersion is wellquasi-ordered for finite graphs. Their proof uses the results of graph minors theory. Surprisingly, there is a very short proof of a corresponding rough structure theorem for graphs without Kt-immersions; it is based on the Gomory-Hu theorem. The same proof also works to establish a rough structure theorem for Eulerian dig...
متن کاملForbidding Kuratowski Graphs as Immersions
The immersion relation is a partial ordering relation on graphs that is weaker than the topological minor relation in the sense that if a graph G contains a graph H as a topological minor, then it also contains it as an immersion but not vice versa. Kuratowski graphs, namely K5 and K3,3, give a precise characterization of planar graphs when excluded as topological minors. In this note we give a...
متن کاملA note on clique-width and tree-width for structures
We give a simple proof that the straightforward generalisation of clique-width to arbitrary structures can be unbounded on structures of bounded tree-width. This can be corrected by allowing fusion of elements.
متن کاملA note on the Chvátal-rank of clique family inequalities
Clique family inequalities a ∑ v∈W xv + (a − 1) ∑ v∈W ′ xv ≤ aδ form an intriguing class of valid inequalities for the stable set polytopes of all graphs. We prove firstly that their Chvátal-rank is at most a, which provides an alternative proof for the validity of clique family inequalities, involving only standard rounding arguments. Secondly, we strengthen the upper bound further and discuss...
متن کاملForbidding and enforcing on graphs
We define classes of graphs based on forbidding and enforcing boundary conditions. Forbidding conditions prevent a graph to have certain combinations of subgraphs and enforcing conditions impose certain subgraph structures.We say that a class of graphs is an fe-class if the class can be defined through forbidding and enforcing conditions (fe-system). We investigate properties of fe-systems and ...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2013
ISSN: 1077-8926
DOI: 10.37236/2533